Okay, a few suggestions and comments.
First, nice strategy, as always.
Second, set the speed required for the second pet to > 341.
There are many beast pets available that are 340, but use them at your own risk. Its a coin flip to see which pet goesfirst and if it favours the enemy team you're going to have the same problems as you would if your pet were simply slower.
Third, take advantage of a potential Devour by the cub on the second enemy pet when possible.
FInally, your TD Script has Shell Shield in the priority list, but it's absent in the strategy instructions.

I used Xu-Fu, Cub of Xuen in my 2nd slot (2,1,2). After the zandalari anklerender dies, Have xu-fu prowl then feed. He was back up to full and the 2nd boss pet was gibbed instantly. Then I had Xu-Fu Bite until he died, taking the final boss pet down to like 1/3rd health. I brought in a Cinder Pup last with Flame Breath and one of those finished him off =)

Thank you for this suggestion! Worked first try! I used a P/S Kneebiter with Xu-Fu and Cinder Pup. Only needed one Flame Breath from Cinder Pup at the end, Xu-Fu had nearly taken out the last two pets himself!

Had trouble with this one, I ended up going with a Zandalari Anklerender cause that was faster than my kneebiter, and following suggestion above, put fox in and used Crouch, Dazzling Dance, and then Flurry until the fox died. The speed buff from Dazzling Dance got me to the kill. Achievement completed!

Not sure if this was RNG, but I failed the first time, so the I change Turn 1 and 2 of Lesser twisted around. First Black Claw then Leap. By doing this, I was able to get a second leap off. Then I raked with Cheetah, then Devoured with Chetah. The second devour killed Lesser Twisted, plus I got healed. I was then able to rake and pounce on Mind warper. Almost didn't need the third pet.

First attempt was close but enemy had 50hp left. I switch Cheetah (s/s) with Panther (s/b) and that worked for me. s/b Panther got a tiny more hp off last enemy helping Infernal Pryeclaw which can only get 2 attacks out.

I had all the cats at 25 except the cheetah, but I couldn't get any of them to work so I ended up using a stone on my cheetah cub. It worked first try. I also had to use an anklerender instead of a kneebiter.